-(4) to the power of 2

Therefore, the sampling distribution will be centered around 0.01, with a standard deviation of 0.0098.

In a random sample of 500 toys from the manufacturer batch, the fraction of defective toys will have a sampling distribution that is roughly normal.

The population proportion of defective toys will be used as the sampling distribution's mean, which is 1% or 0.01. This is thus because a proportion of the sample is a fair estimate of a proportion of the population.

The following formula can be used to determine the standard error, also known as the standard deviation, of the sample distribution:

SE is equal to sqrt[(p*(1-p))/n]

where n is the sample size, 500, and p is the population proportion of faulty toys, which is 0.01.

These values are substituted into the formula to produce:

SE is equal to sqrt[(0.01*(1-0.01))/500] = 0.0098

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Answer:

The semi-circles form an entire circle with a diameter of 74.

The radius is 37

The area of the rectangle is 95 x 74 = 7030

The area of the circle is 3.142 x 37*37 = 4298.66

The total area is 11328.66

The correct formula for the general term of the arithmetic sequence representing the cost of the venue hire and catering for n guests is 1950 + 100n.

To find the formula for the general term of the arithmetic sequence representing the cost of the venue hire and catering for n guests, we can analyze the given information.

We are given two data points: the cost for 50 guests, which is $6,950, and the cost for 100 guests, which is $11,950. We can observe that the difference between these two costs is $11,950 - $6,950 = $5,000.

Since the cost forms an arithmetic sequence, the difference between consecutive terms will remain constant. In this case, the difference is $5,000.

Now, we need to find the initial term of the sequence. By examining the cost for 50 guests, we notice that the difference between the cost for 50 guests and the initial term is $6,950 - $5,000 = $1,950.

Putting it all together, we have the formula for the general term of the arithmetic sequence: initial term + (difference × (n - 1)).

Plugging in the values, the formula becomes: 1,950 + (5,000 × (n - 1)) = 1,950 + 5,000n - 5,000 = 5,000n - 3,050. Simplifying further, we get the final formula: 5,000n - 3,050.

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Answer:

y = -6 x I think

Step-by-step explanation:

please give brainliest I tryed

Answer:

150

Step-by-step explanation:

150

Percentage Calculator: 135 is what percent of 90? = 150.

1945 men and 2849 women register to audition for a singing competition. The number of participants who are not successful in their auditions what’s five times the number of those who are successful. There are 799  participants were successful.

The successful  participants  can be calculate by solving a linear equation as follows

First, it's crucial to understand linear equations.

Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between the two algebraic expressions.

Linear equations are those with one degree.

In this case, a linear equation must be resolved.

1945 for the men's total

Women are present in 2849.

Participants in total: 1945 + 2849 = 4794

Let x be the proportion of participants that were successful.

Men who failed were 5 times as numerous.

Participants in total: 5x + x = 6x

Due to the issue,

The linear formula is

6x = 4794

x = 4794/6

x = 799

799 of the participants had success.

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Answer:

D. subtracted 60 from both sides

Step-by-step explanation:

Step 1: 315= 15p +60

Step 2: 315 - 60 = 15p

Step 3: 255=15p

Step 4: 255/15 = 15p/15

Step 5: p=17

Answer: D. subtracted 60 from both sides

Step-by-step explanation:

How does someone get from 315 = 15p + 60 to 255 = 15p? To solve 315 = 15p + 60, we would need to isolate the variable p.

To isolate the variable p, the first step in solving the equation would be to subtract 60 from both sides; it would look like this:

> Step 2: 315 - 60 = 15p + 60 - 60

If you solve this out, you get:

> Step 3: 255 = 15p

Step two subtracts 60 from both sides of step one to achieve step 3.

Answer:

Equation: 15 + 6t = 81

Work: 15 + 6t = 81

         -15          -15

         6t = 66

           t = 11

<3 love your channel tommyinit

(a) `|r| > 1`, the given geometric series does not converge.

(b) Sum of the given telescoping series is 4τ(n² + 5n + 6).

The given question involves two parts, let's solve them one by one.

(a)n Σ (7) 5

Here, we have to find out if the given geometric series converges or not and its sum.

A geometric sequence is one in which each term is obtained by multiplying the preceding term by a constant factor.Here, the common ratio is `r = 5`

Here, the first term `a = 7`

To check whether a geometric series converges or not, we check the absolute value of the common ratio, if it is less than 1, the series will converge.

Here, `|r| = 5`.As, `|r| > 1`, the given geometric series does not converge.

(b) Find the sum of the telescoping series 2 Σ Στ (n+1)(n+4) n=0

Here, we have to find the sum of the telescoping series:2 Σ Στ (n+1)(n+4) n=0

Let's expand the expression inside the sum and see if it has a pattern that can help us simplify it.

Στ (n+1)(n+4) = τ(1+5) (2+5) + τ(2+5) (3+5) + ....+ τ(n+1) (n+4) (n+2+5) = τ[6 + 3(7)] + τ[3(7) + 4(8)] + ....+ τ[(n+1)(n+4) + (n+3)(n+6)]

The terms inside the parentheses of the last two factors are identical, so we can express the whole sum as

2 Σ Στ (n+1)(n+4) n=0= 2 Σ[τ(6 + 3(7)) + τ(3(7) + 4(8)) + ....+ τ[(n+1)(n+4) + (n+3)(n+6)]]= 2τ[(6 + 3(7)) + (3(7) + 4(8)) + ....+ (n+1)(n+4) + (n+3)(n+6)]

Here, we have used the formula of the telescoping series which is as follows:

Sn = a1 + a2 + a3 + ....+ an-1 + an

Sn = (a1 - a1) + (a2 - a1) + (a3 - a2) + ....+ (an-1 - an-2) + (an - an-1)

Sn = a1 - a0 + a2 - a1 + a3 - a2 + ....+ an-1 - an-2 + an - an-1

Sn = a1 - a0 + an - an-1

As, the series inside the summation contains both even and odd terms which will cancel each other, hence only the first and the last terms of the series will contribute to the sum of the telescoping series.

So, the sum of the given telescoping series is:

2τ[(n+1)(n+4) + (n+3)(n+6)] = 2τ[2n² + 10n + 12] = 4τ(n² + 5n + 6)

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Answer:

47.49%

Step-by-step explanation:

profit / selling price ×100% = gain percent

profit =selling price - cost price

therefore profit = 155.63 - 105.52 = 50.11

50.11/105.52 ×100% = gain percent

47.49% = gain percent

The total calories burned during the workout and walk is 967 calories.

To calculate the total calories burned during a workout and a subsequent walk, the formula is Total calories burned = Calories burned during the workout + Calories burned during the walk.

In this case, the workout burned 712 calories. After the workout, the person took a walk that burned 255 calories per hour. The duration of the walk is not given, so let’s assume that the person walked for 1 hour.The calories burned during the walk are 255 calories per hour, and the duration of the walk is 1 hour.

Therefore, the calories burned during the walk are:

255 calories/hour × 1 hour

= 255 calories

The total calories burned during the workout and walk can now be calculated by using the formula:

Total calories burned = Calories burned during the workout + Calories burned during the walk

Total calories burned = 712 calories + 255 calories

Total calories burned

= 967 calories

Therefore, the total calories burned during the workout and walk is 967 calories.

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Answer:

B. A cube with side lengths of 4ft has a volume of 64 cubic feet.

Step-by-step explanation:

The best interpretation of the function is that a cube with a side length of 4ft has a volume of 64ft³;

    Function;

           v(s) = s³

s is the side of the cube;

   Now, if we input 4, the cube is 64

A function simply relates a set to another one.

So, answer choice B is the right one

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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a) If each plant is required to reduce its pollution by 5,000 tonnes, we can calculate the pollution control costs for each firm using the given marginal cost curves. For Plant 1, MCC1 = 0.02Q, where Q represents the tonnes of pollution reduction. Similarly, for Plant 2, MCC2 = 0.03Q.

For both firms, since the pollution reduction is fixed at 5,000 tonnes, we substitute Q = 5,000 into the respective marginal cost curves:

MCC1 = 0.02 * 5,000 = $100

MCC2 = 0.03 * 5,000 = $150

Therefore, Plant 1's pollution control costs will be $100 and Plant 2's pollution control costs will be $150.

The graph for Plant 1 will have a linearly increasing slope starting from the origin, and the graph for Plant 2 will have a steeper linearly increasing slope starting from the origin.

b) With a pollution tax of $120 per tonne of pollution emitted, each firm's pollution reduction costs will be affected. The firms will now have to pay the pollution tax in addition to their pollution control costs.

Without considering taxes, Plant 1's pollution control costs were $100, and Plant 2's costs were $150 for a total of $250. However, with the pollution tax, the costs will change. Let's assume the firms still need to reduce their pollution by 5,000 tonnes.

For Plant 1: Pollution control costs = MCC1 * Q = 0.02 * 5,000 = $100 (same as before)

Total costs for Plant 1 = Pollution control costs + (Tax per tonne * Tonnes of pollution emitted)

Total costs for Plant 1 = $100 + ($120 * 5,000) = $610,000

Similarly, for Plant 2: Pollution control costs = MCC2 * Q = 0.03 * 5,000 = $150 (same as before)

Total costs for Plant 2 = Pollution control costs + (Tax per tonne * Tonnes of pollution emitted)

Total costs for Plant 2 = $150 + ($120 * 5,000) = $750,000

The total pollution reduction costs with the tax are now $610,000 for Plant 1 and $750,000 for Plant 2, resulting in higher costs compared to part a. This difference arises because the tax imposes an additional financial burden on the firms based on their emissions.

To support this answer, we can draw two graphs, one for each firm, with the tonnes of pollution emitted on the x-axis and the total costs on the y-axis. The graphs will show an increase in costs due to the tax.

c) In a tradable permit scheme where 6,000 permits are issued, with 3,000 permits to each plant, the pollution reduction costs to each firm without trading can be determined.

Since Plant 1 and Plant 2 each receive 3,000 permits, they can each emit up to 3,000 tonnes of pollution without incurring any additional costs. However, if they need to reduce their pollution beyond the allocated permits, they will have to incur pollution control costs as calculated in part a.

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Answer:

-8

Step-by-step explanation:

Let's first establish the reference line (the one that the second line will be perpendicular to).  We are told that this line passes through two points:

(1,1) and (-3,-1).

We'll find a line equation using the point slope form format to start:  

(y - y1) = m * (x - x1), where m is the slope and the x and y are from two points.

(x,y) = (1,1)

(x1,y1) = (-3,-1)

Rearrange the equation:

(y - y1) = m * (x - x1)

m = (y - y1)/ (x - x1)

m = (1-(-1))/(1-(-3))

m = 2/4, or 1/2:  The slope is 1/2.    [This is "m."]

We can use the slope-intercept form for this line (y=mx + b) and then calculate b, the y-intercept:

y = (1/2)x + b

Use either of the two given points.  I'll use (1,1) since I have memorized the "1" math tables.

y = (1/2)x + b  

1 = (1/2)(1) + b for (1,1)

b = 1/2

This makes the reference line:  y = (1/2)x+(1/2)

===

The line perpendicular must have a slope that is the negative inverse of (1/2).  This would be -(2/1), or -2.

We can then write y = -2x + b

To find be, enter the one given point for this line:  (-3,-2)

y = -2x + b

-2 = -2(-3) + b

-2 = 6 + b

b = -8

The perpendicular line is thus:

y = -2x - 8

It has a y-intercept of -8

Let us assume that the decimal representation of $\frac{n}{1375}$ terminates and let $k$ be the number of digits after the decimal point.

Then, $1375 = 5^3 \cdot 11 \cdot 5$ and $n = 5^a\cdot 11^b\cdot 7^c$ , where $a,b,c$ are nonnegative integers. Therefore, $\frac{n}{1375} = \frac{5^{a-3}\cdot 11^{b}\cdot 7^c}{1}$, where $a \le 3$ and $b \le 1$ since the decimal representation of $\frac{n}{1375}$ terminates. Hence, we can consider all values of $n$ of the form $5^a\cdot 11^b\cdot 7^c$, where $a \le 3$ and $b \le 1$ to be integers between $1$ and $1000$ inclusive, whose decimal representation of $\frac{n}{1375}$ terminates. Since $a$ has four choices $(0,1,2,3)$ and $b$ has two choices $(0,1)$, the number of integer values of $n$ between $1$ and $1000$ inclusive, whose decimal representation of $\frac{n}{1375}$ terminates is $4\cdot 2 \cdot 1 = \boxed{8}.$

We want to determine the number of integer values of $n$ between $1$ and $1000$ inclusive that satisfy $\frac{n}{1375}$ has a terminating decimal representation. We use the following fact: A positive rational number has a terminating decimal representation if and only if its denominator can be expressed as $2^a5^b$, where $a$ and $b$ are nonnegative integers.Let $d = \gcd(1375, n)$. Then, $d$ is a positive divisor of $1375 = 5^3 \cdot 11 \cdot 5$. We must have $d = 5^a11^b$, where $0 \leq a \leq 3$ and $0 \leq b \leq 1$ since $d$ divides $n$.We also have that $n = d \cdot k$ for some integer $k$.Thus, the problem is equivalent to counting the number of positive divisors of $1375$ that are of the form $5^a11^b$, where $0 \leq a \leq 3$ and $0 \leq b \leq 1$.

The prime factorization of $1375$ is $5^3 \cdot 11 \cdot 5$. Thus, $1375$ has $4 \cdot 2 \cdot 2 = 16$ positive divisors. We exclude $1$ and $1375$ as possibilities for $d$. Thus, there are $14$ possibilities for $d$. Furthermore, each divisor of $1375$ can be written in the form $5^a11^b$ where $0 \leq a \leq 3$ and $0 \leq b \leq 1$.

Therefore, there are $\boxed{8}$ values of $n$ that satisfy the condition.

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Answer:

see explanation

Step-by-step explanation:

CY = CB + BY

     = 6b + 5a - b

     = 5a + 5b

---------------------

CX = CA + AX

     = CA + \(\frac{1}{3}\) AB , find AB

AB = AC + CB

     = - 3a + 6b

     = 6b - 3a

Thus

CX = CA  + \(\frac{1}{3}\) AB

      = 3a + \(\frac{1}{3}\)(6b - 3a)

      = 3a + 2b - a

      = 2a + 2b

---------------------

and

\(\frac{2}{5}\) CY

= \(\frac{2}{5}\) (5a + 5b)

= 2a + 2b = CX

Hence CX = \(\frac{2}{5}\) CY ⇒ Proven

Answer: 27 1/2 pages per hour

Step-by-step explanation:

if Carrie reads

12 min ........................5 1/2 pages

60 min........................5*(5 1/2) pages=27 1/2 pages

the answer is 10m deep after rising

Emily runs at the fastest speed of 15 ft per second, Liz runs at 13.03 ft per second, and Zack runs at 12.8 ft per second.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that Emily runs 15 ft per second no one runs 358 ft and 36 seconds Liz runs 1 mi in 405 seconds Zack runs 768 feet in 1 minute.

Emily's speed = 15 ft/sec

Liz's speed = 1 mile per 405 sec = 5280/405 = 13.03 ft /sec

Zack's speed = 768 / 60 = 12.8 ft /sec

Therefore, Emily runs at the fastest speed of 15 ft per second, Liz runs at 13.03 ft per second, and Zack runs at 12.8 ft per second.

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If we call `to_pounds(9, 12)`, it will return 9.75, as 9 pounds and 12 ounces is equivalent to 9.75 pounds.

Here's a method called `to_pounds` that takes in the number of pounds and ounces as integers and returns the total weight in pounds as a decimal.

```python

def to_pounds(pounds, ounces):

   return pounds + (ounces / 16)

```

In the method, we divide the number of ounces by 16 to convert them into decimal representation of pounds. This is because there are 16 ounces in a pound.

We then add this value to the given number of pounds, resulting in the total weight in pounds as a decimal. For example, if we call `to_pounds(9, 12)`, it will return 9.75, as 9 pounds and 12 ounces is equivalent to 9.75 pounds.

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Answer:

The y intercept

Step-by-step explanation:

The initial force between the two charges is given by:

\(F=k\frac{q_{1} q_{2} }{d^2}\)

where k is Coulomb's constant, q1 and q2 are the two charges, and d is their separation. Let's analyze now the other situations:

1. F

In this case, q1 is halved, q2 is doubled, but the distance between the charges remains d.

So, we have:

q'₁=q₁/2

q'₂=2q₂

d'=d

So, the new force is:

\(F'=k\frac{q'_{1}q'_{2} }{d^2} \\\\F'=k\frac{(\frac{q_{1} }{2})(\frac{q_{2} }{2}) }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{d^2} =F\)

So the force has not changed.

2. F/4

In this case, q1 and q2 are unchanged. The distance between the charges is doubled to 2d.

So, we have:

q'₁=q₁

q'₂=q₂

d'=2d

So, the new force is:

\(\\F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{2d^2} \\\\F'=\frac{1}{4} k\frac{q_{1}q_{2} }{d^2} \\\\F'=\frac{F}{4}\)

So the force has decreased by a factor of 4.

3. 6F

In this case, q1 is doubled and q2 is tripled. The distance between the charges remains d.

So, we have:

q'₁=2q₁

q'₂=3q₂

d'=d

So, the new force is:

\(F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{2q_{1}3q_{2} }{d^2}\\ \\F'=6k\frac{q_{1}q_{2} }{d^2} =6F\)

So the force has increased by a factor of 6.

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Answer:

1. F

2. F/4

3. 6F

Answer:

1494.64

Step-by-step explanation:

Divide 28 by 2 = 14

14 times 3.14 times 34

I hope thats right

Answer:

834.230769231 or 834.2

Step-by-step explanation:

Answer:

834.10

Step-by-step explanation:

Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

The probability that the equipment will operate for at least 200 hours without failure is \((1-e^{-2} )^2[2e^-2+1]\).

Given:

mean = 1/100

Let X = the number of components that fail before 200 hours . The X has a binomial distribution n = 3 and p = 1 – e^-2.

probability p = 3/2\(p^{2} (1-p)\) + 3/3 \(p^{3}\).

= 3(\(1-e^-2)^2\)\(e^-2\) + (\(1-e^-2)^3\)

= \((1-e^-^2)^2[3e^-^2 - e^-^2+1]\)

= \((1-e^{-2} )^2[2e^-2+1]\)

Therefore the probability that the equipment will operate for at least 200 hours without failure is \((1-e^{-2} )^2[2e^-2+1]\).

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Answer:

               \(\bold{\underline{x\in(-\infty\,,\,-4\big>\cup\big<6\,,\,\infty)}}\)

Step-by-step explanation:

\(\bold{2|x-1|\geqslant10}\\\\{}\ \div2\qquad\div2\\\\\bold{|x-1|\geqslant5}\\\\\bold {x-1\geqslant5\qquad\quad\vee\qquad x-1\leqslant-5}\\\\\bold {x\geqslant6\qquad\qquad\vee\qquad\ \ x\leqslant-4}\\\\\bold{\underline{x\in(-\infty\,,\,-4\big>\cup\big<6\,,\,\infty)}}\)